Furthermore, according to the proof in Ref. [1]}, the yield \({Y_{11,L}^{ZZ}}\)  and the phase-flip error \(e_{11,U}^{ph}\)  in signal states satisfy:
\(\begin{split}{Y_{11,L}^{ZZ}} = {{Y_{11,L}^{XX}}},\qquad \qquad \end{split}\begin{split}e_{11,U}^{ph} = {e_{11,U}^{XX}}.\end{split}\) 
